1. Field of the Invention
This invention relates to a method of interpolation and/or enhancement of data that is a function of two coordinates and more particularly to a method of interpolation and/or enhancement of seismic data traces.
2. Description of the Related Art
Certain forms of data may be represented as multiple data samples in two dimensions. Such a collection of data samples may be referred to as a panel of data.
This invention provides a solution to two related problems. In one, the separate data samples (signals) may not be frequent or regular enough, in either or both coordinates, to enable an interpreter of that data to perform higher levels of processing due to spatial aliasing. In the second, noise in the data samples may mask the information the interpreter is analyzing.
In interpreting and processing data recorded on seismic traces it is preferable that the traces be evenly spaced, sufficiently close together and free of noise. However, in the acquisition of seismic data it may not be possible to meet these criteria due to surface obstacles, cost or equipment failure. Missing traces must then be interpolated and/or various processing techniques used to reduce the noise.
Interpolation methods generally attempt to estimate a new trace by connecting the troughs and peaks representing reflected arrivals in recorded traces along a dip. A dip can be considered to be in this case a rate of change in time of arrival per trace or the slope of a straight line connecting the reflected arrivals on a panel of data. These methods typically examine the recorded traces along a preselected number of trial dips in order to determine the correct dip of the reflected arrivals. From this, a reflected arrival can be estmated for or assigned to the interpolated trace. Alternatively, interpolated traces may be generated by inserting zero traces at the interpolation locations followed by the use of an appropriate spatial filter. However, this alternate approach requires that the dips be approximately known and not aliased with respect to each other.
These methods are insufficient in determining an interpolated trace in the presence of multiple dips and spatial aliasing in the recorded traces. Spatial aliasing is defined as the condition where a dip is so great and the trace spacing so large that it is not possible to unambiguously correlate the peaks and troughs in successive recorded traces. This usually occurs when the peaks and/or troughs on successive traces are at least one-half cycle out of phase. These methods may also fail when the recorded traces exhibit a plurality of widely different dips because of an inability to adequately separate the reflected arrivals.
In addition, many of these methods fail to provide a technique which can be used to enhance the data by selectively using arrivals on traces which have a corresponding arrival on adjacent traces that are related by a dip thereby removing noise from the traces.